Inference Pain Point 1 - The question

Statistical Inference is the practice of forming judgments about the parameters of a population on the basis of random sampling.

When it comes to the inference standards I see 3 main pain points. 

1. The question
2. Sampling variability
3. Answering the question.

In this post I will address pain point 1. The question

The question being asked is about groups within a population. The population being investigated should be identified within the question.

Contextual knowledge drives the investigative process. Spending time developing students contextual knowledge helps students develop their question. 

The senior secondary guides state at 

• NCEA Level 1:  students should be working with contexts that are familiar to them.
• NCEA Level 2:  students should be provided with relevant contextual knowledge about the situation under investigation.
• NCEA Level 3: students should be sourcing relevant contextual knowledge about the situation under investigation from internet, library, newspapers journals…

The Kiwi data on census at school makes a great teaching data set for 2.9. The context is relevant. The web is full of information about the kiwi. 

This video about a kiwi recovery programme at Lake Waikaremoana is sure to engage students in the context. 

source: You tube Endangered KIWI recovery programmes Marae Investigates 13 May 2012 TVNZ

and another from Northland  http://www.maoritelevision.com/news/regional/new-technology-boosts-kiwi-bird-recovery 


Back to the question

The analysis that is possible at each level drives the style of the investigative question.

• At Level 6 (NCEA Level 1, AS 91035) the analysis enables students to investigate whether a variable for one group tends to be bigger than that variable for another group in the population.
• At Level 7 (NCEA Level 2, AS 91264) the analysis enables students to investigate whether one population median is bigger than another population median. 
• At Level 8 (NCEA Level 3, AS 91582) the analysis enables students to investigate the size of the difference between two population means/medians through the construction of a bootstrapped confidence interval for the difference of the population medians/means.

About the Kiwifruit harvest this time...
What might a question look like at each level?
Note: I wonder ... is just one of many ways to begin the question

91035: about a tendency
... I wonder if green kiwifruit tend to be heavier than gold kiwifruit from the 2016 harvest in the Te Puke Region?

91264: moving to a population parameter, the median

... I wonder if the median weight of green kiwifruit is more than than the median weight of gold kiwifruit from the 2016 harvest in the Te Puke Region?

91582: measuring the difference between the medians or means

... I wonder what the size of the difference between the median weight of green kiwifruit and the median weight of gold kiwifruit from the 2016 harvest in the Te Puke Region?

Check: variables, groups, population, comparison 

A prediction or hypothesis is a useful component of the investigative process. 
After writing the question a hypothesis can be made as to what is expected to be found in the investigation. This helps with linking the analysis of the graphs to the question. It also offers students the opportunity to reflect in their conclusion or may even be the catalyst for further investigation. 

More information Link to standard summaries for 91035, 91264,91582

A "sideways map" for 91035

A Facebook Group   for New Zealand statistics teachers

Resources on CensusAtSchool NZ  

next post pain point 2 - sampling variability